5,623 research outputs found
A constrained scheme for Einstein equations based on Dirac gauge and spherical coordinates
We propose a new formulation for 3+1 numerical relativity, based on a
constrained scheme and a generalization of Dirac gauge to spherical
coordinates. This is made possible thanks to the introduction of a flat
3-metric on the spatial hypersurfaces t=const, which corresponds to the
asymptotic structure of the physical 3-metric induced by the spacetime metric.
Thanks to the joint use of Dirac gauge, maximal slicing and spherical
components of tensor fields, the ten Einstein equations are reduced to a system
of five quasi-linear elliptic equations (including the Hamiltonian and momentum
constraints) coupled to two quasi-linear scalar wave equations. The remaining
three degrees of freedom are fixed by the Dirac gauge. Indeed this gauge allows
a direct computation of the spherical components of the conformal metric from
the two scalar potentials which obey the wave equations. We present some
numerical evolution of 3-D gravitational wave spacetimes which demonstrates the
stability of the proposed scheme.Comment: Difference w.r.t. v1: Major revision: improved presentation of the
tensor wave equation and addition of the first results from a numerical
implementation; w.r.t. v2: Minor changes: improved conclusion and figures;
w.r.t. v3: Minors changes, 1 figure added; 25 pages, 13 figures, REVTeX,
accepted for publication in Phys. Rev.
The ideal of the trifocal variety
Techniques from representation theory, symbolic computational algebra, and
numerical algebraic geometry are used to find the minimal generators of the
ideal of the trifocal variety. An effective test for determining whether a
given tensor is a trifocal tensor is also given
State-space Geometry, Statistical Fluctuations and Black Holes in String Theory
We study the state-space geometry of various extremal and nonextremal black
holes in string theory. From the notion of the intrinsic geometry, we offer a
new perspective of black hole vacuum fluctuations. For a given black hole
entropy, we explicate the intrinsic state-space geometric meaning of the
statistical fluctuations, local and global stability conditions and long range
statistical correlations. We provide a set of physical motivations pertaining
to the extremal and nonextremal black holes, \textit{viz.}, the meaning of the
chemical geometry and physics of correlation. We illustrate the state-space
configurations for general charge extremal black holes. In sequel, we extend
our analysis for various possible charge and anticharge nonextremal black
holes. From the perspective of statistical fluctuation theory, we offer general
remarks, future directions and open issues towards the intrinsic geometric
understanding of the vacuum fluctuations and black holes in string theory.
Keywords: Intrinsic Geometry; String Theory; Physics of black holes;
Classical black holes; Quantum aspects of black holes, evaporation,
thermodynamics; Higher-dimensional black holes, black strings, and related
objects; Statistical Fluctuation; Flow Instability.
PACS: 02.40.Ky; 11.25.-w; 04.70.-s; 04.70.Bw; 04.70.Dy; 04.50.Gh; 5.40.-a;
47.29.KyComment: 28 pages. arXiv admin note: substantial text overlap with
arXiv:1102.239
Positivity bounds on gluon TMDs for hadrons of spin 1
We consider the transverse momentum dependent gluon distribution functions
(called gluon TMDs) by studying the light-front gluon-gluon correlator,
extending the results for unpolarized and vector polarized targets to also
include tensor polarized targets -- the latter type of polarization is relevant
for targets of spin . The light-front correlator includes
process-dependent gauge links to guarantee color gauge invariance. As from the
experimental side the gluon TMDs are largely unknown, we present positivity
bounds for combinations of leading-twist gluon distributions that may be used
to estimate their maximal contribution to observables. Since the gluonic
content of hadrons is particularly relevant in the small- kinematic region,
we also study these bounds in the small- limit for the dipole-type gauge
link structure using matrix elements of a single Wilson loop.Comment: 10 page
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